{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/differential-properties-of-sinkhorn","title":"Differential Properties of Sinkhorn Approximation for Learning with Wasserstein Distance","arxiv_id":"1805.11897","date":"2018-05-30","proceeding":"NeurIPS 2018 12","authors":["Giulia Luise","Alessandro Rudi","Massimiliano Pontil","Carlo Ciliberto"],"abstract":"Applications of optimal transport have recently gained remarkable attention\nthanks to the computational advantages of entropic regularization. However, in\nmost situations the Sinkhorn approximation of the Wasserstein distance is\nreplaced by a regularized version that is less accurate but easy to\ndifferentiate. In this work we characterize the differential properties of the\noriginal Sinkhorn distance, proving that it enjoys the same smoothness as its\nregularized version and we explicitly provide an efficient algorithm to compute\nits gradient. We show that this result benefits both theory and applications:\non one hand, high order smoothness confers statistical guarantees to learning\nwith Wasserstein approximations. On the other hand, the gradient formula allows\nus to efficiently solve learning and optimization problems in practice.\nPromising preliminary experiments complement our analysis.","url_abs":"http://arxiv.org/abs/1805.11897v1","url_pdf":"http://arxiv.org/pdf/1805.11897v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"differential-properties-of-sinkhorn","repo_url":"https://github.com/GiulsLu/OT-gradients","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"differential-properties-of-sinkhorn","repo_url":"https://github.com/nicolasbolle/barycenters","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1805.11897","atlas_url":"https://app.syntology.ai/?focus=1805.11897","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}